Question

graph the solution of the following inequality.
4x² - 2x + 2 < 2x² + 14
use the tools to enter your answer.
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Explanation:

Step1: Simplify the inequality

Subtract \(2x^{2}+14\) from both sides:
\(4x^{2}-2x + 2-(2x^{2}+14)<0\)
\(4x^{2}-2x + 2 - 2x^{2}-14<0\)
\(2x^{2}-2x-12<0\)
Divide through by 2: \(x^{2}-x - 6<0\)

Step2: Factor the quadratic

Factor \(x^{2}-x - 6\):
\(x^{2}-x - 6=(x - 3)(x+2)\)
So the inequality is \((x - 3)(x + 2)<0\)

Step3: Find the critical points

Set \((x - 3)(x + 2)=0\)
\(x-3=0\Rightarrow x = 3\) and \(x+2=0\Rightarrow x=-2\)

Step4: Test intervals

• For \(x<-2\) (e.g., \(x=-3\)): \((-3 - 3)(-3+2)=(-6)\times(-1)=6>0\)
• For \(-2
• For \(x>3\) (e.g., \(x = 4\)): \((4 - 3)(4+2)=(1)\times6=6>0\)

Answer:

The solution of the inequality \(4x^{2}-2x + 2<2x^{2}+14\) is \(-2